Simple emergent power spectra from complex inflationary physics

We construct ensembles of random scalar potentials for $N_f$ interacting scalar fields using non-equilibrium random matrix theory, and use these to study the generation of observables during small-field inflation. For $N_f={\cal O}({\rm few})$, these heavily featured scalar potentials give rise to power spectra that are highly non-linear, at odds with observations. For $N_f\gg 1$, the superhorizon evolution of the perturbations is generically substantial, yet the power spectra simplify considerably and become more predictive, with most realisations being well approximated by a linear power spectrum. This provides proof of principle that complex inflationary physics can give rise to simple emergent power spectra. We explain how these results can be understood in terms of large $N_f$ universality of random matrix theory.